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A q-Analogue of the Berezin Quantization Method

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Abstract

We use Berezin's quantization procedure to obtain a formal \(U_q \mathfrak{s}\mathfrak{u}_{11}\)-invariant deformation of the quantum disc. Explicit formulae for the associated bidifferential operators are produced.

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References

  1. Bayen, F., Flato, M., Fronsdal, C., Lichnerovich, A. and Sternheimer, D.: Deformation theory and quantization, Ann. of Phys. 111 (1978), part I: 61-110, part II: 111-151.

    Google Scholar 

  2. Berezin, F. A.: General concept of quantization, Comm. Math. Phys. 40(2) (1975), 153-174.

    Google Scholar 

  3. Chari, V. and Pressley, A.: A Guide to Quantum Groups, Cambridge Univ. Press, 1995.

  4. Cahen, M., Gutt, S. and Rawnsley, J.: Quantization on Kähler manifold III, Lett. Math. Phys. 30 (1994), 291-305.

    Google Scholar 

  5. Klimek, S. and Lesniewski, A.: A two-parameter quantum deformation of the unit disc, J. Funct. Anal. 115, (1993), 1-23.

    Google Scholar 

  6. Klimyk, A. and Schmüdgen, K.: Quantum Groups and Their Representations, Springer, Berlin, 1997.

    Google Scholar 

  7. Koelink, H. T.: Yet another basic analogue of Graf's addition formula, J. Comput. Appl. Math. 68 (1996), 209-220.

    Google Scholar 

  8. Shklyarov, D., Sinel'shchikov, S. and Vaksman, L.: On function theory in quantum disc: integral representations, e-print: math.QA/9808015.

  9. Shklyarov, D., Sinel'shchikov, S. and Vaksman, L.: On function theory in quantum disc: covariance, e-print: math.QA/9808037.

  10. Shklyarov, D., Sinel'shchikov, S. and Vaksman, L.: On function theory in quantum disc: a q-analogue of the Berezin transform, e-print: math.QA/9809018.

  11. Sinel'shchikov, S. and Vaksman, L.: On q-analogues of bounded symmetric domains and Dolbeault complexes, Math. Phys. Anal. Geom. 1 (1998), 75-100; e-print 1997, q-alg/9703005.

    Google Scholar 

  12. Unterberger, A. and Upmeier, H.: The Berezin transform and invariant differential operators, Comm. Math. Phys. 164 (1994), 563-598.

    Google Scholar 

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Authors and Affiliations

  1. Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin Avenue, 61164, Kharkov, Ukraine

    D. Shklyarov, S. Sinel'shchikov & L. Vaksman

Authors
  1. D. Shklyarov
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  2. S. Sinel'shchikov
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  3. L. Vaksman
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Shklyarov, D., Sinel'shchikov, S. & Vaksman, L. A q-Analogue of the Berezin Quantization Method. Letters in Mathematical Physics 49, 253–261 (1999). https://doi.org/10.1023/A:1007675907997

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